Sharendipity is a site that lets you create your own games and then upload them to the site, embed them into other websites or just use games that other people have developed.

Their website states:

Sharendipity is the fun and easy way to create fun, social games without programming that can be shared with your friends or embedded on your website. Or simply browse and play the creations of others, challenging your friends to beat your high score! Create a game in four easy steps or try the advanced game creator!

There is a wiki and a blog to assist if you need it as well as a forum to consult other Sharendipity members. Looks like fun for teachers and students alike.